Solve the Differential Equation $$x \frac { d y } { d x } = \frac { \cos x } { x ^ { 5 } } - 6 y , x > 0$$

question 68

Multiple Choice

Solve the differential equation.
- $$x \frac { d y } { d x } = \frac { \cos x } { x ^ { 5 } } - 6 y , x > 0$$

• A) \(y = x ^ { - 6 } ( \cos x + C ) , x > 0\)
• B) \(y = x ^ { 6 } ( \sin x + C ) , x > 0\)
• C) \(y = x ^ { 6 } ( \cos x + C ) , x > 0\)
• D) \(y = x ^ { - 6 } ( \sin x + C ) , x > 0\)

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Definitions:

Unconscious Material

Content of the mind that is outside of conscious awareness, including desires, thoughts, and memories, which can influence behavior and perceptions.

Ego

In psychoanalysis, it represents the part of the personality that mediates between the conscious and unconscious aspects of oneself and is responsible for reality testing and a sense of personal identity.

Id's Drives

Fundamental, unconscious urges and desires, often related to survival and pleasure, according to Freudian psychoanalytic theory.

Superego's Prohibitions

Restrictions or moral imperatives imposed by the superego, a component of Freud's psychoanalytic theory representing internalized ideals and morals.